Ten Years of Gurevich's Abstract State Machines

State Machines have come quite a way since they have been discovered by Yuri Gurevich in an attempt to improve on Turing's thesis so that: Every algorithm can be simulated in lock{step on its natural abstraction level by an ASM. The rst years after the de nition of ASMs appeared in the literature (under the name of dynamic or evolving algebras, see [Gurevich 1988]) were characterized by an impressive number of challenging experiments to test this bold thesis through complex real-life case studies, ranging from semantics and implementation of full edged programming languages to speci cation and veri cation of protocols and hardware designs. The rst full de nition and careful motivation for the new notion appeared in 1991 in the Bulletin of the EATCS and was completed four years later by a solid foundation and an extension to distributed ASMs (see [Gurevich 1995]). The rst international ASM workshop|held as part of the IFIP 1994 World Computer Congress in Hamburg with an unexpectedly great number of participants|has marked the end of this rather successful exploratory phase. The interested reader can nd a detailed overview in the ASM chapter of the congress proceedings (see [Pehrson and Simon 1994]) and through the annotated bibliography which covers the ASM literature completely up to the end of 1994 (see [Borger 1995a]). In a relatively short time the ASM approach to speci cation and veri cation of complex hw/sw systems has proved its feasability for real-life problems and is now establishing its feasability to applications under industrial constraints. The ourishing ASM research is steadily growing as is documented in this special J.UCS issue which is devoted entirely to ASMs and came into life through a call for papers sent out last year. The great number of submissions which passed the reviewing process forced us to split the special ASM issue into two parts, one issued in April and one in May. The papers in this issue deal with foundational questions, with questions from complexity theory, with the central notion of re nement and with machine support for reasoning about ASMs. The paper on Recursive Abstract State Machines by Gurevich and Spielmann presents an interesting use of distributed ASMs to interpret recursive calls as creating slaves of the calling program. Thus the usual stack which is hidden by the very concept of recursion and is used only for its implementation is re ected (although hidden) in the the master/slave hierarchy of the distributed ASM. This construction allows one to view recursive notation as mere abbreviation and thereby to combine the convenience of the use of recursion with the advantage of the simple semantical foundation of the basic ASM notion which deliberately has no built-in concept of sequencing, loop or recursion. Two papers deal with complexity theoretic questions. The paper on The Linear Time Hierarchy by Blass and Gurevich suggests a new approach for attempts Journal of Universal Computer Science, vol. 3, no. 4 (1997), 230-232 submitted: 20/12/96, accepted: 21/4/97, appeared: 28/4/97  Springer Pub. Co.